Application of the non-uniform Fourier transform to non-uniformly sampled Fourier transform spectrometers

Resampling by interpolation is the traditional method to process interferograms from non-uniformly sampled Fourier transform spectrometers. The non-uniform fast Fourier transform (NUFFT) is an alternative approach that has been mostly overlooked. With the aid of experiments on a high-resolution interferometer with a variety of optical sources, these two methods are compared. It is found that the NUFFT is comparable to interpolation in spectral profile shape and spectral noise levels and is better in spectral amplitude and computer performance. A significant advantage is also found in the case of under-sampling and noise performance by NUFFT due to the unique non-periodic nature of non-uniform sampling. In addition, a novel implementation of NUFFT is presented and analysed.